Question

48xy^4 - 72xy^2
------------- < divided line
12xy^2
A. 4xy2 - 6xy2
B. 4y2 - 6
C. 4xy - 6y
D. 4y - 6

Answer 1

\[\frac{48xy^4-72xy^2}{12xy^2}\]Treat the coefficients and variables separately. Let's do the coefficients first. You're just going to look at the 48, -72, and 12 first.

Answer 2

What's the greatest common factor for those three numbers?

Answer 3

72 is not negative ? but is 72 the greatest common factor ?

Answer 4

A common factor is a number that will divide into all three numbers. What can you divide 48, 72, and 12 by?

Answer 5

No lie i don't even know ?

Answer 6

No worries!

For example, 2 goes evenly into 48, 72, and 12. Same thing with 3.

Answer 7

So the way to start these problems is to look at what you can "pull out" of all the numbers.

Answer 8

so 3 &2 both go into 48,72,12 evenly ?

Answer 9

Exactly. So does 6. If we divide each number by 6, we get 8 (from 48), 12 (from 72), and 2 (from 12).

With me so far?

Answer 10

so you got 8 outta 48 and 12 outta 72 & 2 outta 12 ?

Answer 11

Right. So here's what this means. Instead of writing
\[\frac{48xy^4-72xy^2}{12xy^2}\]you could write
\[\frac{8xy^4-12xy^2}{2xy^2}\]which definitely looks a little nicer

Answer 12

Now what do i do from there ?

Answer 13

Now, the numbers aren't completely reduced. What's the common denominator for 8, 12, and 2?

Answer 14

4 goes in to 8 & 6 goes into 12 and 2 goes in to 2 ?

Answer 15

Those divide evenly into the numbers, but what you're looking for is a single number that goes into all of them. 2 goes into all three of the numbers, so that's the number you're looking for. Even though 4 goes into 8, 4 doesn't go into 2.

When you pull out a 2 from each one, you get
\[\frac{4xy^4-6xy^2}{1xy^2}\]
Now let's look back at the original problem. It was possible to pull out a 12 at the very beginning, which would have gotten us here in one step instead of two steps. 12 was the largest number that would have gone into 48, 72, and 12. That means that 12 is our least common denominator.

Let me know when you're ready to go on.

Answer 16

Oops, I typed "least common denominator." What I meant was "greatest common factor."

Answer 17

Okay im ready

Answer 18

Alright. Now we're going to ignore the original problem. All we care about now is this:
\[\frac{4xy^4-6xy^2}{xy^2}\]because we made it easier to deal with.

Now we're going to mess with the variables.

Answer 19

You're concerned now with the xy^4, xy^2, and xy^2. Treat the x's separately from the y's. Each term has one x. We can basically just cancel all of them out. Now we have
\[\frac{4y^4-6y^2}{y^2}\]
Okay with that?

Answer 20

yeah so the answer is 4y2-6

Answer 21

Yep :)

Answer 22

Thank's alot

Answer 23

No problem. Good luck.

Answer 24

Thank's lol ill be pack tomorrow with like 90 more questions

Answer 25

Back *

Answer 26

Ew, sorry about that.